If I were police chief, that officer would be off the force, on the grounds that he acted foolishly and tarnished the department’s good name. The family would receive a check reimbursing them for the dog without prompting.
Though noble, and I agree wholeheartedly with your sentiment, it would just create an even bigger problem. In court it would be viewed as an outright admission of guilt, and open the police department to further lawsuits, basically giving the victims a blank check and the city and police department no defense.
Secondly, the officer involved will also sue for wrongful termination. His defense will always be that he was defending himself. It will be the onus of the department to prove him wrong.
So on the one hand, you do whats right, admit fault and get sued by the victims, with no defense, THEN you also get sued by the officer, and thus get your butt fired by the mayor. Or, you swallow the bile in your throat, and cover your, the city's, the department and the cops collective asses.